Problem: Solve for $a$, $ -\dfrac{3a + 10}{2a + 2} = -\dfrac{2}{2a + 2} + \dfrac{1}{10a + 10} $
Solution: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2a + 2$ $2a + 2$ and $10a + 10$ The common denominator is $10a + 10$ To get $10a + 10$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{3a + 10}{2a + 2} \times \dfrac{5}{5} = -\dfrac{15a + 50}{10a + 10} $ To get $10a + 10$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ -\dfrac{2}{2a + 2} \times \dfrac{5}{5} = -\dfrac{10}{10a + 10} $ The denominator of the third term is already $10a + 10$ , so we don't need to change it. This give us: $ -\dfrac{15a + 50}{10a + 10} = -\dfrac{10}{10a + 10} + \dfrac{1}{10a + 10} $ If we multiply both sides of the equation by $10a + 10$ , we get: $ -15a - 50 = -10 + 1$ $ -15a - 50 = -9$ $ -15a = 41 $ $ a = -\dfrac{41}{15}$